A long-time friend, who did not wish to be identified, said Mr White was a "rare breed" who was impossible to dislike, and "definitely very loved".
"Honestly, there is nothing bad you can say about him, if he was to see you crying he would stop everything to make sure you were OK," the friend said.
"A little cheeky, heartwarming, made sure that you were home safe, made sure that you were doing well, always checking up."
The friend said Mr White, who he has known for seven years, was experienced in roofing work.
"It's so tragic, very unexpected, you don't really expect that to happen to anyone, it just shows our time here is very short and can come at any moment," the friend said.
Another friend paid tribute to Mr White's "cheeky grin", saying he would be "deeply missed".
Other friends said he was "gone way too soon" and was "one of a kind".
NSW Ambulance Inspector Andy Cullen said on Monday afternoon it was a difficult operation to recover Mr White, involving specialist paramedics and Fire and Rescue NSW crews.
"It was a challenging situation to reach the final patient who was still up on the roof," Inspector Cullen said on Monday afternoon.
Electricity to the building had to be turned off before emergency crews could access the roof and Mr White. By that time, Inspector Cullen said: "the patient was found to be unfortunately deceased".
The inspector said he had been told Mr White "was holding some kind of metal pole in his hand, and he's turned and inadvertently touched some live wires adjacent to the rear of the building".
A SafeWork NSW spokeswoman said investigations into the incident were ongoing.
"Preliminary enquiries suggest the worker suffered fatal injuries after coming into contact with overhead power lines," she said.
Police are also investigating the incident, and a report on Mr White's death will be prepared for the Coroner.